Collect the default WordPress Website URL and Biographical description during Membership Checkout with Register Helper fields using save_function custom callback that includes a validation check which returns an error message if the field value failed the check.

example-pmprorh-save-function-with-registration-check.php

<?php
/**
 * This recipe adds Website and Biographical Info to the Membership Checkout.
 *
 * You can add this recipe to your site by creating a custom plugin
 * or using the Code Snippets plugin available for free in the WordPress repository.
 * Read this companion article for step-by-step directions on either method.
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */

function my_default_wp_user_checkout_fields() {
	if ( class_exists( 'PMProRH_Field' ) ) {

		// create custom checkout box
		pmprorh_add_checkout_box( 'additional', 'Additional Information' );

		// Conditional to show on your profile and hide on user edit profile
		$your_profile = false;
		if ( ! is_admin() ) {
			$your_profile = true;
		}

		// create array.
		$fields = array();

		// user_url field
		$fields[] = new PMProRH_Field(
			'url',
			'text',
			array(
				'label'         => 'Website url', // Change label here
				'size'          => 40, // Change size here
				'profile'       => $your_profile, // Hide on profile page
				'required'      => false, // Make field optional (set to true to make required)
				'save_function' => 'my_pmprorh_callback_update_my_user_url', // Custom callback to save field values
			)
		);

		// user_description field
		$fields[] = new PMProRH_Field(
			'description',
			'textarea',
			array(
				'label'         => 'Biographical Info', // Change label here
				'profile'       => $your_profile, // Hide on profile page
				'required'      => false, // Make field optional (set to true to make required)
				'save_function' => 'my_pmprorh_callback_update_usermeta_textarea',
				'sanitize'      => false,
			)
		);

		foreach ( $fields as $field ) {
			pmprorh_add_registration_field( 'additional', $field );
		}
	}
}
add_action( 'init', 'my_default_wp_user_checkout_fields' );

function my_pmprorh_callback_update_my_user_url( $user_id, $field_name, $field_value ) {

	// update wp_user table
	wp_update_user(
		array(
			'ID'       => $user_id,
			'user_url' => esc_url_raw( $field_value ),
		)
	);
	// duplicate value in wp_usermeta table so RH can access field value
	update_user_meta( $user_id, $field_name, esc_url_raw( $field_value ) );
}

function my_pmprorh_callback_update_usermeta_textarea( $user_id, $field_name, $field_value ) {

	// santize text area content
	$txtarea = wp_kses( $field_value, wp_kses_allowed_html( 'pre_user_description' ) );

	update_user_meta( $user_id, $field_name, $txtarea );
}

// Check if url starts with protocol and
function my_pmpro_check_valid_url( $pmpro_continue_registration ) {
	// bail if not okay to continue
	if ( ! $pmpro_continue_registration ) {
		return $pmpro_continue_registration;
	}

	if ( isset( $_REQUEST['url'] ) ) {

		// get url field value
		$url = $_REQUEST['url'];

		// check if it starts with protocol
		if ( ! empty( $url ) && 1 <= strpos( $url, 'http' ) ) {

			// things are not okay
			$pmpro_continue_registration = false;

			// notify user on checkout page.
			pmpro_setMessage( 'Please enter a full URL starting with http:// or https:// ' . strpos( $url, 'http' ), 'pmpro_error' );
		}
	}

	return $pmpro_continue_registration;

}
add_filter( 'pmpro_registration_checks', 'my_pmpro_check_valid_url' );

For capturing URL and Biographical Info without an additional registration and validation check see:
https://gist.github.com/ipokkel/2f88849447f85175eb161b19d4551119

For capturing URL only Info see:
https://gist.github.com/ipokkel/6590d29c21e41a49e7e2577fe9ca7955